Recent months have seen some coverage of the “fossil fuel divestment” movement, backed by the Guardian and the fossilfreeindexes.com website. One particular campaign has called for organisations to freeze new investments in the top 200 publically-traded fossil fuel companies. Such campaigners hope that by encouraging investors to avoid fossil fuel stocks and bonds, the amounts of fossil fuels produced and consumed will fall, and that this will lead to fewer carbon emissions.

Setting aside, for now, issues regarding the effectiveness of such a strategy in itself or the desirability of its objectives, two questions of importance for investors considering fossil fuel divestment are: first, how much would this cost? And, second, once one knows much it would cost, is this the best way to spend that money in trying to achieve the desired end?

At Europe Economics, we have estimated what the costs to investors of a divestment strategy would have been up to now. The most important general investor cost of refusing to invest in fossil fuels is that such investors limit their ability to “diversify” their investments.

Diversification is a familiar concept in ordinary life, seen in proverbs such as “Don’t put all your eggs in one basket.” Investors diversify to offset certain risks. For example, if oil prices sky-rocket during a Middle East war, that may be bad for many economic investments, including those that depend on low inflation, for example. But when oil prices are high, oil producers tend to do better. So just when investments in low-inflation-dependent products are falling in value, investments in oil stocks may be rising in value. So someone wanting to invest in low-inflation-dependent products might, at the same time, invest in some oil stocks to reduce the risk.

If investors are unable to use fossil fuel stocks to offset risks, their total portfolio risk will rise unless they are able to find something else to use instead. But are the alternatives as good. And, if not, what is the cost?

In our study released recently, we measured the cost of the risk-return trade-off of removing a significant set of players in the FTSE. We used this theory to construct two sets of stocks: one a broad tracker based on the stocks in the FTSE All Share Index, and the other with the listed fossil fuel firms excluded. Within those two sets, we established the set of ‘efficient portfolios – those for which there was no way to enjoy greater returns without facing more risk.

Comparing the two sets of ‘efficient portfolios’ – divested and not – we found that investors who want to exclude fossil fuels will need to pick their poison: 20 per cent more risk if they want to avoid any reduction in returns, 68 basis points less in returns each year if they want to avoid any additional risk on their portfolio, or some mix of the two.

Let’s make that finding more concrete. If someone had £100,000 invested in a pension pot tracking the stock market from 2002 they would have had about £280,000 in 2014. If, instead, they had excluded fossil fuels in 2002 then by 2014 they would have had only £260,000 – a loss of more than seven per cent over the period. Even at a low four per cent rate, the £280,000 pension pot would yield an £11,200 a year pension, against £10,400 for the £260,000 pension pot. If someone had that kind of private pension, they would therefore be losing £800 a year by divesting fossil fuel stocks.

To some, the feeling that “something has been done” might be worth some investment loss. But a significant proportion of investors considering fossil fuel divestment may have the impression that it would be possible to pursue such a strategy without significant financial losses. According to a recent poll conducted by FTI Consulting, 23 per cent of the UK public said they would not be willing to sacrifice anything by adopting a divestment strategy, while a combined 46 per cent would be willing to sacrifice less than £100 a year.

‘Diversification’ is a central concept of finance theory, and our findings confirm that – as one would intuitively expect – fossil fuel stocks are crucial to the construction of risk-balanced portfolios. We note again that our study focused on the potential financial impact of a divestment strategy and not whether such a strategy would achieve the goals of climate activists seeking to send a message to fossil fuel companies. They may very well have sent a message, but that message would come at a cost. Investors need to consider whether the strategy is sufficiently likely to achieve its ends to be worth that cost and, even if it is, whether that is the most effective way to spend this amount of money, given the alternative ways in which funds could be used to promote environmental ends.